CP - Tools for Proofs Lesson

Tools for Proofs

You now have many of the skills and tools needed in order to build a proof.   In this lesson, we are going to look at a couple of other tools, as well as some common situations you may run into while building your proofs. These are some of the more commonly used tools, but remember that you can use any rule or definition that you already know to be true in order to complete a proof.

Reflexive Property

What can you say about segments BD and DB?

The reflexive property is called reflexive because what it tells you is reflexive or automatic. Since BD and DB are the same segment, of course they are congruent. The Reflexive Property can be used to state any angle or segment that two triangles share is congruent in each of the triangles.

Check out the video below to see the reflexive property in action.

Triangle Sum Theorem

You may have already learned about the sum of the angles in a triangle.

If you already know that two pairs of corresponding angles in a pair of triangles are congruent, you can use the triangle sum theorem to prove that the third pair must also be congruent.

Substitution

The Substitution Property is a property that you are already familiar with. You have used it in the past to help solve equations. Check out this video to see how substitution works.

CPCTC

Once you know that two triangles are congruent, you then can be assured logically that all of their corresponding parts are congruent.

Corresponding Parts of Congruent Triangles are Congruent

This can be used to prove that angles or segments are congruent after we already know two triangles are congruent.

The following video will show you how these different tools for proofs can be used together. 

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